1. Field of the Invention
The invention concerns techniques for determining a radio-frequency pulse, for example a multichannel radio-frequency pulse, for magnetic resonance imaging. In particular, the invention relates to techniques of the type wherein an approximation is made of a vector that represents a spatial region in which transverse magnetization is to be influenced by the radio-frequency pulse.
2. Description of the Prior Art
In magnetic resonance (MR) imaging, transverse magnetization of nuclear spins in an examination subject is influenced, i.e. excited or refocused, by the irradiation or transmission of a radio-frequency (RF) pulse. Excitation of the transverse magnetization typically means deflection of the nuclear spins from their equilibrium position along the longitudinal direction, which can be defined, for example, by the basic magnetic field (B0 field) and locally acting perturbation fields that occur due to susceptibility changes. Usually, large-area whole body transmitting coils, for example, are used for radiating the RF pulses. Such whole-body coils have dimensions on the order of magnitude of the actual object under examination. The RF magnetic field (B1 field) generated by the transmission is then substantially constant or homogeneous along the object under examination.
However, it is also possible to use multiple RF transmitting coils in a coil array that have comparatively small dimensions. Time-parallel transmission of the identical, individual RF pulses via the different transmitting coils enables a spatially-selective influence on the transverse magnetization. Here, the transverse magnetization can be influenced in a well-defined, specified spatial region by specific data entry points in the spatial frequency domain (k-space) being passed through (traversed) during the transmission, i.e. along a specific k-space trajectory.
Recently, it has also been possible in this regard to use so-called multichannel RF pulses within the context of parallel transmission (pTX). To this end, typically individual, different RF pulses, that combine to form the multichannel RF pulse, are transmitted by the different RF transmitting coils of the coil array. A multichannel RF pulse can make it possible to generate different time-dependent B1 fields that are well-defined with respect to phase or amplitude, at different spatial positions in the object under examination. pTX enables the sampling requirement of the Nyquist theorem to be broken (not satisfied) and the necessary scanning of (entry of MR data into) the k-spaces, and hence also the duration of the multichannel RF pulse, to be significantly reduced, by a degree that is called TX acceleration.
In addition, pTX techniques have advantages in connection with high-field MR systems with which the basic magnetic field has a high field strength, for example 3 tesla or 5 tesla or more. In such cases, the specific absorption rate (SAR) of the RF exposure for the patient can be reduced by the use of multichannel RF pulses. It is also possible to compensate inhomogeneities of the B1 field more effectively.
However, known techniques of this kind can also be associated with certain restrictions and disadvantages. For example, it can typically be necessary to determine the individual RF pulses, i.e. a temporal sequence of the voltage signal applied to different RF transmitting coils of the coil array, of which the multichannel RF pulse is composed, shortly before the performance of MR imaging, for example as a function of different measured and/or preset operating parameters of the MR system, in particular already in the presence of the object under examination in the MR system. To this end, it is possible, for example, to solve an equation corresponding to equation (3) in DE 10 2012 207 132 B3. However, this can require a high computing capacity. For example, depending upon the desired spatial resolution and/or temporal resolution of the RF pulse to be determined, it may be necessary to handle a data volume in the order of magnitude of gigabytes. Typically, it can be necessary to invert a system matrix or design matrix of this order of magnitude which reflects the operating parameters etc. in order to invert a linear equation system.
In this context, it is known to use a wide variety of digital-signal-processing or linear-algebra techniques to reduce the amount of computational effort required. It is often the case, however, that techniques of this kind are not able to reduce the required computational effort significantly and/or represent a comparatively strong approximation of the problem, which can result in undesirably high inaccuracies or errors in the solution.
For example, techniques are known from S. Feng and J. X. Ji, “An Algorithm for Fast Parallel Excitation pulses Design” in Proc. Intl. Soc. Mag. Reson. Med 21 (2013) 4255 relating to more extensive simplifying assumptions when determining multichannel RF pulses. For example, it is known from this article by Feng et al. to limit the size of entries of a system matrix in that contributions are rejected if they only make a small energy contribution to the solution. In this case, for example, spatial frequencies with a low contribution to the spatial region to be excited, which are regularly the higher spatial frequencies, are rejected. As a result, it is in turn possible to reduce the dimensions of the system matrix to be inverted. However, this typically results in a restriction of the accuracy to be achieved since finer details in the multichannel RF pulse are not taken into account or only restrictedly taken into account thus causing the spatial region actually excited to be smeared or blurred. The reason is that typically contributions contributing to high spatial frequencies are not taken into account.
For example, techniques are known from DE 10 2011 005 174 A1 that also relate to simplifying assumptions when determining multichannel RF pulses. For example, the format of the result vector representing the temporal course of the multichannel RF pulse can be restricted in that it is determined as a linear combination of precompiled basis functions of a decomposition. As a result, it is in turn possible to reduce the dimensions of the system matrix to be inverted, in particular the number of its columns. However, the result is a restriction of the achievable accuracy since the degrees of freedom with respect to which the result vector is optimized are restricted. For example, the compensation of B1 field inhomogeneities and/or B0 field inhomogeneities on the determination of a multichannel RF pulse cannot be considered or only considered to a limited extent, which can result in significant artifacts and quality losses in the excited spatial region.
Therefore, there is a need for improved techniques for the determination of RF pulses, in particular for improved pTx techniques. In particular, there is a need for techniques that permit a relatively low computationally intensive determination of the RF pulses. There is also a need for techniques that allow a relatively precise and flexible determination of the RF pulses.